4.ideal Reactors 591a4

CONTINUOUS IDEAL REACTORS

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Continuous Stirred Tank Reactor

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CSTR Contd. . .

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CSTR Animation

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• Also called as Mixed, Backmix, Ideal stirred tank reactor • Open system, operates under steady state conditions • Reactants are continuously introduced and products are

continuously withdrawn • Perfect mixing – contents have uniform properties – No spatial variations • Conditions at the exit are same as inside the reactor • Used for homogenous liquid phase reactions where

constant agitation is required • Eg. Sulfonation, Polymerization, plastics, explosives, synthetic rubber etc. CSTR Contd. . .

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Advantages: • Cheap to construct

• Good temperature control • Reactor has large heat capacity • Easy access to interiors Disadvantages: • Conversion per unit volume of the reactor is smallest compared to other flow reactors

CSTR Contd. . .

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Fractional Conversion (xA): FA0  FA xA  FA0 C A0  C A (for constant density) xA  C A0 Space time ():

Space time is the time required to process one reactor volume of inlet material (feed) measured at inlet conditions.  is the time required for a volume of feed equal to the volume of the vessel (V) to flow through the vessel.  = V/v0 = sec N.B. : Volume of vessel here means volume of Reaction Mixture.

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Space Velocity (S): Space velocity (S) is the reciprocal of space time, the number of reactor volumes of feed, measured at inlet conditions, processed per unit time. Mean Residence time tm:

The residence time is the length of time species spend in the reactor. All molecules that enter may not spend the same time in the reactor. The distribution of residence times – RTD The average length of time that molecules spend in the reactor – mean residence time (tm) tm = V/vE 8

FA  FA0 (1  x A ) v0  FA0 / C A0

lit mol mol   sec sec lit

For constant density: FA FA0 (1  x A ) CA    C A0 (1  x A ) v v0 For variable density: FA FA0 (1  x A ) (1  x A ) CA    C A0 v v0 (1   A x A ) (1   A x A )

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Stoichiometric Table – Flow Systems aA + bB  rR + sS Species

A B R S I

Total

Initial

FA0

FB0 FR0 FS0 FI0

FT0

Change -FA0xA -(b/a)FA0xA +(r/a)FA0xA +(s/a)FA0xA 0

Final moles FA= FA0(1-xA) FB= FA0(MB-(b/a)xA) FR= FA0(MR+(r/a)xA) FS= FA0(MS+(s/a)xA) FI = FI0

FT = FT0 + NA0δxA

Where: MI = FI0/FA0 δ = (r/a + s/a – b/a – 1)

For Constant density: CA = CA0(1-xA)

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Design Equation General Mass Balance Equation: Rate of Input = rate of output + accumulation + rate of disappearance FA0 = FA + 0 + (-rA) V FA0 - FA = (-rA) V

FA0 CA0 v0

FA CA V xA

FA0 xA = (-rA) V V / FAo = xA / -rA 12

General Design eqn. for a CSTR: V / FAo = xA / -rA V / (v0 CA0) = xA / -rA  / CA0 = xA / -rA Design eqn. for a CSTR under constant density:  = (CA0 – CA) / -rA

tm = V/vE

Note that the space time and the mean residence time are equal only in the case of constant density. 13

DA =kCA0n-1 

Comparison of Different order Reactions in a CSTR

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Plug Flow Reactor

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The necessary and sufficient condition for plug flow is the residence time in the reactor to be the same for all elements of the fluid.

PFR Animation

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• PFR is also called as tubular reactor • Residence time is same for all fluid elements

• Operated under steady state conditions • Reactants are consumed as they flow down along the length of the reactor • Axial concentration gradients exist • One long tube or a number of short tubes (see fig.)

• Choice of diameter depends on fabrication cost, pumping cost and heat transfer needs • Wide variety of applications in gas/liquid phase • Eg.: Production of gasoline, cracking, synthesis of ammonia, SO2 oxidation

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(1) The flow in the vessel is Plug flow. (2)There is no axial mixing of fluid inside the vessel (i.e., in the direction of flow). (3)There is complete radial mixing of fluid inside the vessel (i.e., in the plane perpendicular to the direction of flow). (4)Properties may change continuously in the direction of flow (5)In the axial direction, each portion of fluid, acts as a closed system in motion, not exchanging material with the portion ahead of it or behind it. 19

Advantages: • Easily maintained as there are no moving parts

• High conversion per unit volume • Unvarying product quality • Good for studying rapid reactions Disadvantages: • Poor temperature control • Hot spots may occur when used for exothermic

reactions PFR Contd. . .

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Design Equation General Mass Balance Equation:

Rate of Input = rate of output + accumulation + rate of disappearance

FA = FA + dFA + 0 + (-rA) dV -dFA = (-rA) dV

FA0 dxA = (-rA) dV

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General Design eqn. for a PFR: xA

V / FA0   dxA /  rA

xA

 / C A0   dxA /  rA 0

0

Design eqn. for a PFR (under constant density): xA

    dCA /  rA 0

V

tm   dV / v 0

Note that the space time and the mean residence time are equal only in the case of constant density. 26

CA/CA0

DA = kCA0n-1 

Comparison of Different order Reactions in a PFR

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Item

BR

CSTR

PFR

XA

(NA0-NA)/NA0

(FA0-FA)/FA0

CA

NA/V

FA/v

-rA

(NA0/V)dxA/dt

t

NA0dxA/V(-rA)

FA0xA/V

FA0dxA/dV  = V/v0

Constant density XA

(CA0-CA)/CA0

-rA

-dCA/dt

t

-dCA/(-rA)

(CA0-CA)/CA0 (CA0 -CA)/

-dCA/d

 = V/v0 28

Algorithm for Isothermal Reactor Design

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CSTR  / CA0 = xA / -rA

PFR x A

 / C A0   dxA /  rA 0

 / CA0

 / CA0 1 /-rA

xA 31

CSTR V / FA0 = xA / -rA

PFR x A

V / FA0   dxA /  rA 0

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CSTR

xA

PFR

    dCA /  rA

 = (CA0 – CA) / -rA

0



 1 /-rA

1 /-rA

CA

CA0

CA

(Constant Density)

CA0

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CSTR

(Constant Density)

PFR 

1 /-rA  1 /-rA

CA

CA0

CVBR CA

CA0

t 1 /-rA

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CA

CA0

CSTR

PFR  / CA0 1 /-rA

 / CA0 xA

VVBR

1 /-rA

1  rA (1   A x A )

t / CA0

xA 35

xA

CSTR

(Constant Density)

PFR

CA

 = (CA0 – CA) / -rA

    dCA /  rA C A0

Zero Order CA

 = (CA0 – CA) / k

    dCA / k C A0

k = CA0 – CA k = CA0 xA

k = CA0 – CA k = CA0 xA Constant Density BR

kt = CA0 – CA

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CSTR

(Constant Density)

CA

 = (CA0 – CA) / -rA

PFR

    dCA /  rA C A0

First Order CA

 = (CA0 – CA) / kCA k = (CA0 – CA)/CA k = xA /(1-xA)

    dCA / kC A C A0 A

C  ln   ln(1  x A )  k C A0

Constant Density BR

CA  ln  kt C A0

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CSTR

(Constant Density)

CA

PFR

    dCA /  rA

 = (CA0 – CA) / -rA

C A0

Second Order CA

 = (CA0 – CA) / kCA

2

    dCA / kC A

2

C A0

k = (CA0 – CA)/CA2 k CA0 = xA /(1-xA)2

1 1   k C A C A0

Constant Density BR

1 1   kt C A C A0

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Constant Density

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For constant density:

• The performance of the Batch reactor is similar to that of PFR for all orders • The performance of all the three reactors is the same in case of zero order reaction • The performance of PFR is superior to that of a CSTR for all orders > 0

For all reaction orders > 0 • The volume of a CSTR required for obtaining a

given conversion is larger than that of PFR • For the same volumes of PFR & CSTR, the conversion obtained is larger in the case of PFR 40

(Variable Density)

CSTR  = CA0xA / -rA

PFR xA

  C A0  dxA /  rA

CA 1  xA  C A0 1   A x A

0

Zero Order xA

 = CA0 xA / k

  C A0  dxA / k 0

k = CA0 xA

k = CA0xA Variable Density BR:

C A0 ln(1   A x A )  k At

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CSTR

(Variable Density)

A

CA 1  xA  C A0 1   A x A

 = CA0xA / -rA

PFR x

  C A0  dxA /  rA 0

First Order xA

 = CA0 xA / kCA

  C A0  dxA / kC A 0

k = CA0 xA/CA

k  (1   A ) ln(1  xA )   A xA

Variable Density BR:

 ln(1  xA )  kt

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CSTR

(Variable Density) CA 1  xA  C A0 1   A x A

 = CA0xA / -rA

PFR xA

  C A0  dxA /  rA 0

Second Order xA

 = CA0 xA / kCA

2

  C A0  dxA / kC A

2

0

k = CA0 xA / CA2

C A0 k  2 A (1   A ) ln(1  x A )

  x  ( A  1) x A /(1  x A ) 2 A A

2

Variable Density BR:

x A (1   A ) /(1  x A )   A ln(1  x A )  kC A0t

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Variable Density

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Relative performance of plug flow and continuous-flow stirred tank reactors

Fraction unreacted is larger in CSTR for a given Da

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Comparison of reactor volume required for a given conversion for a first-order reaction in a PFR and a CSTR

• For small conversions VCSTR/VPFR = 1 (selection of reactor not very critical).

• For large conversions, VCSTR/VPFR is very large (selection of 46 reactor very critical).

For Variable density: • The performance of CSTR & PFR is similar in case of zero order (irrespective of constant / variable density) • The performance of BR is different from the performance of PFR (the performance was similar in the case of constant density) • The performance of PFR is superior to that of a CSTR for all orders > 0 (same as constant density) 47

Comparison of possible advantages (+) and Disadvantages (-) for Batch, CSTR and PFR Reactors

Criteria

Batch

CSTR

PFR

Reactor size for given conversion

+

-

+

Simplicity and Cost

+

+

-

Continuous operation

-

+

+

Large throughput

-

+

+

Cleanout

+

+

-

On-line analysis

-

+

+

Product quality

-

+

+

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ANY CLARIFICATIONS ? Abbey, Edward That which today calls itself science gives us more and more information, an indigestible glut of information, and less and less understanding. 49